salamat po diyos ko at buhay pa kami ng asawa ko

One of my friend had an accident. She posted this on FB : "salamat po diyos ko at buhay pa kami ng asawa ko".
I think it means they are fine but i just understand some words in the sentence.
Could you help me please ?

You meant to say: ....pero hindi ko maintindihan ang at .... ( .... but I can't understand the at)

There is obviously a connection between being grateful to one's God and the fact that one has apparently survived some calamity so the easiest way to think about your text is to consider the conjunction at not as and but as that (Salamat po Diyos ko at buhay pa kami ng asawa ko = Thank you Lord that my spouse and I are still alive).

A more complicated way of examining the same text would be that phrases like salamat po Diyos ko (along with salamat sa Diyos, praise the Lord, Diyos kong maawain / mahabagin, etc.) often have to be taken as religious ejaculations that are separate from the rest of the text. It is in part due to the psyche of a traditionally deeply religious people that would make individuals invoke praises upon, express gratitude towards or implore help from the deity despite whatever else is expressed in the text. Thus, in the phrase: Salamat po Diyos ko at buhay pa kami ng asawa ko --- the speaker is in essence expressing gratitude to God (Thank you Lord), something that a worshipful person is supposed to do constantly anyway no matter what his current circumstances might be. However, in this particular instance, the person is thanking God, and by the way, my spouse and I are still alive. In certain groups, it is not uncommon to hear salamat sa Diyos or especially praise the Lord almost as a preface to whatever else is about to said. As with some other cultures, these religious ejaculations almost become a form of greeting sometimes.

“at “, which is more equivalent to “and”, is less likely used as "a conjunction which connects consequence”,

That you would use “gayon (man) na or gayun na/gayung)” instead. Which simply is equivalent to “now that”.

e.g."salamat po diyos ko at(gayung) buhay pa kami ng asawa ko".

Thus you may translate the original context into:

"Thanks, my God, now that we are alive (with my spouse)."

Note: “God” is separated by two commas to indicate that it is a noun which receives the address or known to be parenthetical word, to follow the structure of the original context. Or else, the original context would go as: "salamat sa diyos at buhay pa kami ng asawa ko"